A researcher conducts a related-sample study to evaluate two treatments with n = 16 participants and obtains a t statistic of t = 1.94. The treatment 2 is expected to have a greater sample mean than the treatment 1. What is the correct decision for a hypothesis test using α =.05?

Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim may be supported.

Step-by-step explanation:

Solution:-

- The sample size of two treatments, n = 16

- The mean of sample treatment 1, u1

- The mean of sample treatment 2, u2

- The significance level, α =.05

- State the hypothesis:

Null hypothesis : u2 - u1 > 0

Alternate hypothesis : u2 - u1 ≤ 0

- The rejection region of the T - critical for lower tailed test.

significance level, α =.05

degree of freedom v = n - 1 = 16 - 1 = 15

T-critical = - 1.75

- The T-test value is compared with T-critical:

T-test = 1.94

T - critical = - 1.75

T-test > T-critical ... (Null not rejected)

- Not enough statistical evidence to prove that treatment 2 sample mean u2 is less than treatment 1 sample mean u1. So the claim maybe supported.